Israel's army said the intercepted rockets on Saturday morning were targeting the Israeli town of Metula.
This is the second time rockets have been fired from Lebanon into Israel since December, sparking concern about whether the fragile ceasefire with the Lebanese militant group Hezbollah would hold.
Hezbollah began launching rockets, drones and missiles into Israel the day after Hamas' October 7, 2023, attack out of Gaza ignited the war there.
The Israel-Hezbollah conflict boiled over into an all-out war in September as Israel carried out massive waves of air strikes and killed most of the militant group's senior leaders.
The fighting killed more than 4000 people in Lebanon and displaced about 60,000 Israelis.
Under the ceasefire reached in November, Israeli forces were supposed to withdraw from all Lebanese territory by late January.
The deadline was then extended to February 18 by agreement between Lebanon and Israel.
But since then, Israel's remained in five locations in Lebanon across from communities in northern Israel and has carried out dozens of air strikes on southern and eastern Lebanon, saying it attacked Hezbollah targets.
Lebanon has appealed to the United Nations to pressure Israel to fully withdraw from the country.
Signalling it could further escalate its response, the Israeli military said on Saturday it would "respond severely to the morning's attack".
Defence Minister Israel Katz said the country would not allow Lebanon to fire into Israeli communities.
"We promised security to the Galilee communities and that is exactly what will happen," he said.
There was no immediate comment from Hezbollah.
In a statement, Lebanon Prime Minister Nawaf Salam asked the Lebanese military to take all necessary measures in the south, but said the country did not want to return to war.
The strikes come a day after Israel said it would carry out operations in Gaza "with increasing intensity" until Hamas frees the 59 hostages it holds, 24 of whom are believed alive.
Israel's military said on Friday its forces were planning fresh assaults into three neighbourhoods west of Gaza City and issued warnings on social media for Palestinians to leave the areas.
Also on Friday, Israel blew up the only specialised cancer hospital in the war-torn territory.
The Israeli military said it struck the Turkish-Palestinian Friendship Hospital, accusing Hamas militants of operating on site.
Turkey, which helped build and fund the hospital, said Israeli troops at one point used it as a base.
About 600 Palestinians have been killed since Israel relaunched the war earlier this week.
Israel had already cut off the supply of food, fuel, and humanitarian aid to Gaza's roughly two million Palestinians, aiming to pressure Hamas over ceasefire negotiations.
The international community has condemned the resumed attacks.
In a statement on Friday, the foreign ministers of the United Kingdom, France and Germany called Israel's strikes in Gaza a dramatic step backward.
"We are appalled by the civilian casualties and urgently call for an immediate return to a ceasefire," they said in a joint statement.
The attack by Hamas-led militants in 2023, killed some 1200 people and took 251 hostages.
Most of the hostages have been freed in ceasefire agreements or other deals.
Israeli forces have rescued eight living hostages and recovered the bodies of dozens more.
Israel's retaliatory offensive has killed more than 49,000 Palestinians, according to the Gaza health ministry.
It does not say how many were militants but says more than half of those killed were women and children.
Israel says it has killed about 20,000 militants, without providing evidence.
